Modeling Emergent Collective Behavior
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Transcript of Modeling Emergent Collective Behavior
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Modeling Emergent Collective Behavior
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We now interrupt this broadcast for breaking news….
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Three Behavioral Zones
•Zone of repulsion
•Zone of orientation
•Zone of attraction
•Blind Regiona
Adapted from Inada, 2002
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The Logic of the ModelIf any neighbors in zone of repulsion (“Dude, quit riding my tail!”).
Else If all neighbors are in the zone of orientation:
If neighbors exist in both orientation and attraction zones:
If all neighbors are in the zone of attraction:
Otherwise fish is lost
Get away--repulsion has highest priority.
Orient to their (average) heading
Come closer to their (average) position
Then orient and get closer, in proper proportion
Turn around 180 degrees and start heading back
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Desired direction for individual i. i = 1, 2, …, N
Repulsion Rule Orientation RuleAttraction Rule
The Three “Laws of Orientation”
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Model Implementation: Compute Desired Heading
If any neighbors in zone of repulsion (repulsion has highest priority!):
Else If all neighbors are in the zone of orientation:
If neighbors exist in both orientation and attraction zones:
If all neighbors are in the zone of attraction:
Otherwise fish is lost, turn 180 degrees-
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Desired turning angle:
If f(t) < wt (Desired turn can be achieved in one time step)
Else (Desired turn cannot be achieved in one time step, turn as much as possible toward desired heading)
Model Implementation: Update Current Heading
Fraction defines how much of desired turn is actually achieved.
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Quantifying group coherencePolarization
Angular Momentum
Moment Arm
Centroid
Average heading
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Couzin Model ResultsCirculating fish school—rare!
Random/disorganized group behavior
Emergent collective behavior: all fish pointed the same direction
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Predator Attack!What rules do you
obey?Move away from
predator?Or stay with the
school?
Obey your thirst!
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Run (errr, swim) for Your Lives!: The Predator Escape Rule
Rpred
Pure predator escape rule
Predator escape with obedience to the school
Obedience parameter (range = 0-1)h = 1: Fully obedient to the schoolh = 0: Ignore the school, move only to get away from predator
If predator is within the ‘danger zone’ (defined by Rpred)
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Predator Attack: Further Considerations
What about multiple predators? And what about ratio of school sizeto number of predators?
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Simulation Software (FishSim)
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ReferencesI.D. Couzin et al. Collective Memory and Spatial Sorting
in Animal Groups, J. theor. Biol (2002) 218, 1-11
Y. Inada and K. Kawachi. Order and Flexibility in Motion of Fish Schools, J. theor. Biol (2002), 214, 371-387
Adi Shklarsh, Gil Ariel, Elad Schneidman, Eshel Ben-Jacob. Smart Swarms of Bacteria-Inspired Agents with Performance Adaptable Interactions. PLoS Computational Biology, 2011; 7 (9): e1002177 DOI: 10.1371/journal.pcbi.1002177
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Definition of Coordinate System